期刊
CLASSICAL AND QUANTUM GRAVITY
卷 36, 期 16, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1361-6382/ab2e13
关键词
Einstein-aether theory; strongly hyperbolic systems; well-posed Cauchy formulations
类别
资金
- European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme [GRAMS-815673]
- European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant [690904]
- CONACyT Network Project [294625]
- CIC
- Perimeter Institute for Theoretical Physics
- Government of Canada through the Department of Innovation, Science and Economic Development Canada
- Province of Ontario through the Ministry of Economic Development, Job Creation and Trade
We study the well-posedness of the initial value (Cauchy) problem of vacuum Einstein-rather theory. The latter is a Lorentz-violating gravitational theory consisting of general relativity with a dynamical time-like 'aether' vector field, which selects a 'preferred time' direction at each space-time event. The Einstein-nether action is quadratic in the anther, and thus yields second order field equations for the metric and the aether. However, the well-posedness of the Cauchy problem is not easy to prove away from the simple case of perturbations over flat space. This is particularly problematic because well-posedness is a necessary requirement to ensure stability of numerical evolutions of the initial value problem. Here, we employ a first-order formulation of Einstein-anther theory in terms of projections on a tetrad frame. We show that under suitable conditions on the coupling constants of the theory, the resulting evolution equations can be cast into strongly or even symmetric hyperbolic form, and therefore they define a well-posed Cauchy problem.
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